Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain

Thierry Gallay[1]

  • [1] Institut Fourier Université de Grenoble 1 100, rue des Maths, B.P. 74 38402 Saint-Martin-d’Hères, France

Journées Équations aux dérivées partielles (2012)

  • page 1-17
  • ISSN: 0752-0360

Abstract

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We study the long-time behavior of infinite-energy solutions to the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. The initial data we consider are finite-energy perturbations of a smooth vortex with small circulation at infinity, but are otherwise arbitrarily large. Using a logarithmic energy estimate and some interpolation arguments, we prove that the solution approaches a self-similar Oseen vortex as t → ∞ . This result was obtained in collaboration with Y. Maekawa (Kobe University).

How to cite

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Gallay, Thierry. "Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain." Journées Équations aux dérivées partielles (2012): 1-17. <http://eudml.org/doc/275561>.

@article{Gallay2012,
abstract = {We study the long-time behavior of infinite-energy solutions to the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. The initial data we consider are finite-energy perturbations of a smooth vortex with small circulation at infinity, but are otherwise arbitrarily large. Using a logarithmic energy estimate and some interpolation arguments, we prove that the solution approaches a self-similar Oseen vortex as $t \rightarrow \infty $. This result was obtained in collaboration with Y. Maekawa (Kobe University).},
affiliation = {Institut Fourier Université de Grenoble 1 100, rue des Maths, B.P. 74 38402 Saint-Martin-d’Hères, France},
author = {Gallay, Thierry},
journal = {Journées Équations aux dérivées partielles},
keywords = {Navier-Stokes equation; long-time behavior; exterior domain},
language = {eng},
pages = {1-17},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain},
url = {http://eudml.org/doc/275561},
year = {2012},
}

TY - JOUR
AU - Gallay, Thierry
TI - Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain
JO - Journées Équations aux dérivées partielles
PY - 2012
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 17
AB - We study the long-time behavior of infinite-energy solutions to the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. The initial data we consider are finite-energy perturbations of a smooth vortex with small circulation at infinity, but are otherwise arbitrarily large. Using a logarithmic energy estimate and some interpolation arguments, we prove that the solution approaches a self-similar Oseen vortex as $t \rightarrow \infty $. This result was obtained in collaboration with Y. Maekawa (Kobe University).
LA - eng
KW - Navier-Stokes equation; long-time behavior; exterior domain
UR - http://eudml.org/doc/275561
ER -

References

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